Take the car to a genuine Audi repair shop where they can scan the OBD computer with proper equipment. Chances are, since you drove through a puddle, that an electrical lead was damaged or moved away from it's proper terminal. This should be relatively easy to find and repair. Be sure to check that your trans fluid is up to it's proper level, and only use genuine Audi trans fluid (which is gold in color because it is mineral based). This shouldn't be an expensive repair, mostly tough to find a knowledgeable person capable enough to deal with it. Good Luck!!!